The Basic Formula for Percent Change

Percent change measures how much a number has grown or shrunk compared to where it started. The formula is: divide the difference between your new number and your old number by the old number, then multiply by 100.

Written as an equation, it looks like this:

(New Number − Old Number) ÷ Old Number × 100 = Percent Change

The result tells you the percentage increase or decrease. A positive result means the number went up. A negative result means it went down.

This formula works for any two numbers: rent prices, income, population, test scores, or housing costs. The steps are always the same.

Key Takeaways

  • Subtract the old number from the new number to find the raw difference.
  • Divide that difference by the old number — this is the crucial step that converts the change into a proportion.
  • Multiply the result by 100 to turn the decimal into a percentage.
  • A positive answer means an increase; a negative answer means a decrease.
  • The old number must never be zero, or the formula breaks down.

Working Through a Real Example

Say your rent was $1,200 last year and is now $1,350. Here's how to find the percent change:

Step 1: Find the difference. Subtract the old number from the new number: $1,350 − $1,200 = $150.

Step 2: Divide by the old number. Take that $150 and divide it by $1,200: $150 ÷ $1,200 = 0.125.

Step 3: Multiply by 100. Convert the decimal to a percentage: 0.125 × 100 = 12.5%.

Your rent increased by 12.5%. This same method works whether the change is an increase or a decrease — if the new number is smaller, you'll get a negative result, which represents a decrease.

When the Change Is a Decrease

If a number goes down instead of up, the formula still works the same way. The negative sign in your answer tells you it's a decrease.

For example, suppose you had $5,000 in savings and now have $4,200. The calculation is: ($4,200 − $5,000) ÷ $5,000 × 100 = −$800 ÷ $5,000 × 100 = −16%.

The negative sign means your savings decreased by 16%. You can also say "your savings dropped by 16%" or "you lost 16% of your savings." All three phrasings mean the same thing.

The direction of change — up or down — is built into the math. You don't have to remember a separate formula for decreases.

Common Mistakes to Avoid

The most frequent error is dividing by the wrong number. You must always divide by the old number, not the new one. Dividing by the new number gives you a different percentage that doesn't mean what you think it does.

Another mistake is forgetting to multiply by 100. If you stop after dividing, you'll have a decimal (like 0.125) instead of a percentage (12.5%). The multiplication by 100 is what converts the decimal into the percentage form people expect to see.

A third pitfall: if the old number is zero, the formula cannot work. You cannot divide by zero. This rarely comes up in housing or income calculations, but it's worth knowing the formula has limits.

Using Percent Change to Compare Different Situations

Percent change is useful because it lets you compare changes that started from different numbers. A $100 increase means something different depending on whether you started with $500 or $5,000.

If your utility bill went from $100 to $150, that's a 50% increase. If someone else's bill went from $200 to $250, that's only a 25% increase. The second person paid more in absolute dollars, but the first person's bill grew faster as a percentage. Percent change shows you the rate of growth, not just the raw amount.

This matters when you're comparing rent increases across different neighborhoods, or when you're looking at how your own costs have changed over time.

Rounding and Decimal Places

Most percent changes come out to a decimal. You can round to whatever precision makes sense for your purpose. For rent or income, rounding to one decimal place (like 12.5%) is usually clear enough. For very small changes, you might keep two decimal places (like 0.75%).

There's no single "correct" number of decimal places. Round to whatever helps you communicate the change without losing important detail. If you're writing a report, pick a consistent number of decimal places and stick with it throughout.

Frequently Asked Questions

What if I have more than two numbers — like rent over five years?

Calculate the percent change between each pair of consecutive years separately. Or, to find the total change from year one to year five, use the first year as your old number and the fifth year as your new number. The formula works the same way.

Can percent change be more than 100%?

Yes. If something doubled, that's a 100% increase. If it tripled, that's a 200% increase. If a number went from $10 to $50, that's a 400% increase. There's no upper limit to how large a percent change can be.

How is percent change different from percentage points?

Percent change measures how much a number grew or shrank relative to its starting value. Percentage points measure the raw difference between two percentages. If unemployment was 5% last year and is 7% this year, it rose by 2 percentage points, but that's a 40% increase in the unemployment rate itself.

Do I need a calculator to do this?

No, but one helps. You can do the math by hand or use a basic calculator, a spreadsheet, or even a phone calculator app. The steps are simple enough to work through on paper if you need to.